<<

. 13
( 39)



>>

is no.

Consider two ¬rms. A has a E(gE ) = 5% growth rate and earnings of $100 (next year); and B
˜ The average of
individual P/E ratios is
has a E(gE ) = 14% growth rate and earnings of $50 (next year). Both have an E(˜) = 15% cost
r
˜ not the overall P/E ratio
of capital. Their respective values should be
$100
P/E =
PA ≡ VA = = $1, 000 ’ 10 ,
15% ’ 5%
(10.19)
$50
P/E = 100 .
PB ≡ VB = = $5, 000 ’
15% ’ 14%

What would happen if these two ¬rms merged into a single conglomerate, called AB? Assume
AB does not operate any di¬erently”the two ¬rms would just report their ¬nancials jointly. AB
must be worth $6,000”after all, nothing has changed, and you know that NPVs are additive. It
would have earnings of $150. Thus, its P/E ratio would be $6, 000/$150 = 40.

PAB (10.20)
= 40 ’ PAB = 40 · EAB .
Correct But Unknown AB P/E ratio:
EAB

Your goal is to value AB. Fortunately, you just happen to know a perfectly comparable ¬rm for
division A (trading at about P/E = 10), and a perfectly comparable ¬rm for division B (trading
at about P/E = 100). You even have a good idea of the relative size of the divisions inside
AB (5:1). Knowing the combined earnings of AB of $150, you want to estimate a value for AB,
based on your two comparables. Unfortunately, neither the unweighted average P/E ratio nor
the weighted average P/E ratio gives you the correct desired P/E ratio of 40:

PA PB
1 1
· + · = 55 ,
Unweighted P/E ratio Average of A and B
EA EB
2 2
(10.21)
PA PB
1 5
· + · = 85 .
Weighted P/E ratio -Average of A and B
EA EB
6 6

Applying either of these two P/E ratios to your $150 in earnings would result in price assess-
ment for AB that would be too high.



Important:

• Price-earnings ratios cannot be averaged.

• Mergers change the P/E ratio, even if they do not create value.



The inability to aggregate divisions is not only an issue for the ¬rm that is to be valued, but it also Lack of easy aggregation
makes it dif¬cult to
makes it di¬cult to extract a single comparable ratio from a division from inside conglomerates.
value even well-de¬ned
In our case, let™s assume that you only wanted to value the U.S. Dr. Pepper division, and that ¬rms, if the comparables
the U.S. Coca-Cola soda division was a perfect comparable for the U.S. Dr. Pepper. But how do are divisions inside
larger ¬rms.
you extract a P/E ratio for the Coca-Cola division, if all you know is the P/E ratio of the overall
Coca Cola company with all its international subsidiaries, Minute Maid, Odwalla, etc.?
¬le=comparables.tex: LP
248 Chapter 10. Valuation From Comparables.

You have no good methods to aggregate and disaggregate P/E ratios. Therefore, strictly speak-
The consequences of the
aggregation failure ing, you can only compare full ¬rms that are similar, which means that P/E ratios are likely
mean, strictly speaking,
to work well only for simple and well-de¬ned companies, and not so well for complex con-
that only the most basic
glomerates. In retrospect, it would have been a coincidence if your naïve attempt to apply the
single-product ¬rms
should be compared.
overall P/E ratio of Coca Cola or PepsiCo to Cadbury Schweppes™s overall earnings would have
worked. Indeed, in retrospect, it was an amazing coincidence that PepsiCo and Coca Cola had
such similar P/E ratios. We lived in blissful ignorance.

In Part III, we will introduce “market-beta” as a valuation measure. Unlike P/E ratios,
market-beta nicely aggregates and disaggregates. This makes it relatively easy to com-
pute betas for conglomerates from their divisions, and to extract a division beta (given
the conglomerate beta and comparable betas for other divisions).




10·3.C. A Major Blunder: Never Average P/E ratios

On top of these unavoidable P/E ratio problems, many an analyst has mistakenly created a
Using a ¬rm with
negative earnings as the much worse and avoidable problem by averaging P/E ratios. Averaging overlooks the fact that
comparable makes
earnings can be (temporarily) zero or negative, which can totally mess up any P/E ratio analysis.
absolutely no sense.
For example, consider the example where the choice of industry comparables for X consists of
A and B.

Value (P) Earnings (E) P/E ratio E/P yield
+$10 ’
Firm A $1,000 100 1.000%
’$5 ’ ’4 ’0.250%
Firm B $20
Industry Average: 48 0.375%
Firm X ? $2

If Firm B were the only comparable, it would imply a negative value for Firm X,

(10.22)
VX = EX · (PB /EB ) = $2 · (’4) = ’$8 .

A value of minus eight dollars for a ¬rm with positive earnings and limited liability is not
sensible. Luckily, this comparables-derived valuation is so nonsensical that no analyst would
not notice it.
But the problem is often overlooked when an analyst uses a P/E industry average. For example,
Averaging P/E ratios can
look reasonable at ¬rst assume our analyst uses an average of both comparables: Firm A has a P/E ratio of 100, Firm B
glance...
has a P/E ratio of ’4. Thus, the average P/E ratio would be 48 (= [100 + (’4)]/2), which is a
reasonable looking average that would not raise a red ¬‚ag. A thoughtless analyst could conclude
that Firm X should be worth VX = EX · (PA,B /EA,B ) = $2 · 48 = $96.
Figure 10.4 makes the absurdity of this method even clearer. What happens to the implied value
...but it is not.
of Firm X if Firm B™s earnings change? As Firm B improves its performance from about ’$5
to about ’$1, the average P/E ratio becomes 40, and your implied value remains a seemingly
reasonable $80. Beyond ’$1, earnings improvements in the comparable B create non-sensically
huge negative implied ¬rm values for X. Then, further improvements suddenly create non-
sensically huge positive ¬rm values. Finally, once the earnings of B are above $1 or so, you
again get seemingly reasonable values (of about $100) for X. So, small changes in earnings
can produce either seemingly sensible or non-sensible valuations. In other examples, even one
comparable with earnings close to zero among a dozen comparables can totally mess up an
average of many comparable P/E ratios.
¬le=comparables.tex: RP
249
Section 10·3. Problems With P/E Ratios.



Figure 10.4. Implied Value vs. Earnings Changes of One Comparable


300
Implied Value of Firm X

200
100
0
’100




’10 ’5 0 5 10

Earnings of Comparable B

If the earnings of the comparable B are $1, you get a sensible value for your ¬rm X. If the earnings are a little bit lower,
you get a non-sensically high number; if the earnings are a little bit lower, you get a non-sensically low number; and
if the earnings are yet a little bit lower, you again get a non-sensical number”but one that can appear at ¬rst glance
to be of reasonable magnitude.




In an e¬ort to deal with this problem, a common industry practice is to drop out ¬rms with Excluding ¬rms does not
help.
non-positive earnings from P/E averages. Unfortunately, this is not a good solution, either. First,
you want an accurate valuation, and the stock market did value Firm B at $20. You have no
good reason to ignore ¬rms with low earnings. Second, dropping out some ¬rms does not
solve the problem: the ¬rm would enter the P/E average if its earnings are +5 cents (leading to
a very high industry P/E average), but be dropped out if its earnings are ’5 cents (potentially
leading to a much lower industry average). A small change in the P/E ratio of one comparable
among the industry would have a disproportionately large impact on comparables valuation
due to arbitrary inclusion/exclusion of comparables, rather than to closeness of earnings to
zero. The reason for all these problems with price-earnings ratios is that earnings are in the
denominator. The function 1/E is both discontinuous and very steep when earnings are close
to zero. In contrast, the price (value) is guaranteed to be positive.
Fortunately, there are two easy overall alternatives to obtain good “pseudo averaged P/E ratios,” The two better
alternatives.
even if some ¬rms™ earnings in the industry are low:

1. Work with earnings yields (E/P yields) instead of P/E ratios.
In the example, the E/P yield of Firm A is $10/$1, 000 = 1%; the E/P yield of Firm B
if it earned ’1 cent is ’$0.01/$20 = ’0.05%. The average E/P yield is thus [1% +
(’0.05%)]/2 = 0.475%. Inverting this back into a P/E ratio provides a halfway sensible
value for the P/E ratio (1/0.475% ≈ 211).

2. Add up all market capitalizations in the industry and all earnings in the industry, and
then divide the two.
In the example where B earned “1 cent, the total industry earnings would be $10.00 ’
$0.01 = $9.99, the entire industry market value would be $1, 000 + $20 = $1, 020, and
¬le=comparables.tex: LP
250 Chapter 10. Valuation From Comparables.

the average P/E ratio would be $1, 020/$9.99 ≈ 102. Note that in this method, ¬rms are
not equally weighted, but weighted by their relative market valuation. This may or may
not be desirable: In our example, ¬rm A would become the dominant determinant of your
comparable valuation ratio.

Neither of these methods will give a very appealing comparable if the total industry average
earnings are very small or negative. Our averaging alternatives can only avoid the problem of
excessive in¬‚uence of a small number of negative (or small) earnings ¬rm in the average.



Important: Although neither P/E ratios nor E/P yields can be averaged, strictly
speaking, an averaging-like operation can often be performed. We do so only
because we lack a better alternative and we do not want to rely on just one single
comparable. Never directly average P/E ratios. Instead

1. Either average E/P yields and then invert,
2. or divide total P sums by the total E sums.

Never take these averages literally. Your goal must be to produce an “intuitively
good (industry) average” derived from multiple comparables, not an exact number.
You may judge your estimation to be better if you omit outlier ¬rms, for example.




10·3.D. Computing Trailing Twelve Month (TTM) Figures

There is one “small” mechanical detail left: Timing. First, is it meaningful to use annual earnings
When comparable ¬rms
report annual for a ¬rm if the last annual report was from eleven months ago? Or should you use just the last
statements in different
quarter™s numbers? Second, some ¬rms report earnings in June, others in December. Should
months, the time change
you compare ¬nancials that are timed so di¬erently, especially if the economy has changed
in economic climate
introduces yet another
during this time lag? For example, consider the following reports:
problem.


2001 2002
Q1 (Mar) Q2 (Jun) Q3 (Sep) Q4 (Dec) Q1 (Mar) Q2 (Jun) Q3 (Sep)
Comparable Firm $1 $2 $3 $9 $5 $6 $7
’ Ann:$15


Your own ¬rm is closing its ¬nancial year with annual earnings of $12 in October 2002. What
are the relevant comparable earnings? Should you compare your own annual earnings of $12
to the dated annual earnings of $15 from December 2001?


Anecdote: What P/E ratio to believe?
Exchange traded funds (ETFs) are baskets of securities, often put together to mimick an index. You can think
of ETFs as ¬rms for which you know the value”and price earnings ratio”of each and every division (stock
component).
On March 13, 2006, the WSJ reported that Barclays Global Investors calculates the P/E ratio of its iShares S&P500
ETF as 16.4 and that of its iShares Russell 2000 ETF as 19.1. The Russell 2000 includes many mid-market ¬rms.
It has garnered nearly $7.5 billion from investors, and is one of the fastest growing funds in 2006. So, the two
funds look comparable in value and/or risk”or do they?
If you compute the weighted sum of the market value of all stocks in the Russell 2000 index and divide that
¬gure by the companies™ total earnings, you ¬nd that this ETF has a P/E Index of 41. Why the di¬erence?
Because the iShares ETF excludes all loss-making companies when calculating the measure”and there were
many Russell 2000 components thus excluded. Karl Cheng, an iShares portfolio manager, says investors don™t
normally look at negative P/E ratios for companies, so they don™t include it in the data. Investors should consider
other measures, he says. Thanks, Karl!
Source: Wall Street Journal, March 13, 2006 (page C3).
¬le=comparables.tex: RP
251
Section 10·3. Problems With P/E Ratios.

You could try to work directly with quarterly earnings, but this is usually not a good idea. Most This time difference can
be reduced, even though
¬rms do more business in December, and December can be the ¬rst month in a quarter or the
quarterly accounting
last month in a quarter. Not only are di¬erent quarters di¬cult to compare across ¬rms, but statements themselves
the fourth quarter may be di¬cult to compare even to the other three quarters of the same ¬rm. should be avoided.
Instead, use quarterlies
So, generally, the best method to adjust ¬‚ows (such as earnings) into a “most recent annualized
and annuals to compute
equivalent” is to use a trailing twelve months (TTM) adjustment. In our example, this means “trailing twelve month”
(TTM) ¬gures.
adding the earnings from Q4-2001 through Q3-2002,

As If Annual in Sep 2002 = $9 + $5 + $6 + $7 = $27
(10.23)
= Q4-01 + Q1-02 + Q2-02 + Q3-02 .
TTM Earnings

Using the reported earnings, you can also compute this

As If Annual = + ($5 ’ $1) + ($6 ’ $2) + ($7 ’ $3) = $27
$15

TTM Earnings = Ann-01 + (Q1-02 ’ Q1-01) + (Q2-02 ’ Q2-01) + (Q3-02 ’ Q3-01) .
(10.24)


There are two caveats: ¬rst, TTM adjusts only “¬‚ow” numbers (such as earnings or sales), “Trailing twelve months”
only works for “¬‚ow”
never “stock” numbers (such as corporate assets). Stock numbers are whatever they have been
numbers (such as
reported as most recently. Second, ¬rms sometimes change their ¬scal year, often to make it income), not for stock
intentionally more di¬cult to compare numbers. In this case, extra care must be exercised. numbers (such as
assets).


10·3.E. Leverage Adjustments For P/E Ratios

This section assumes that riskier projects have to offer higher expected rates of return.
Why this is the case will only fully become clear in Part III. Trust me for now.


Companies can be ¬nanced through a mix of debt and equity. You would want to know if Does leverage in¬‚uence
P/E ratios?
the P/E ratio of a ¬rm is changed by its leverage. If the same ¬rm with more debt in its capital
structure has a di¬erent P/E ratio, then you cannot compare two otherwise identical companies
with di¬erent debt ratios without adjustment.
Return to a simple example. With $100 in annual earnings, a growth rate of 0% now, and an Recapitalizing a 100-0
¬rm into a 50-50 ¬rm.
appropriate cost of capital of 10%, a hypothetical ¬rm A would be worth $1,000. A has no
debt (leverage). We now work out what happens to the price-earnings ratio of A if it were to
recapitalize itself. That is, A takes on a loan of $500, and pays the cash proceeds from the loan
to the equity share owner. This is called a debt-for-equity (or debt-for-stock) exchange. Such
transactions are fairly common.
From Chapter 5, you already know that the cost of capital (interest rate) consists of multiple ...with different costs of
capital for bonds and
components: the time-premium, the default-premium (on average, zero), and the risk-premium.
stocks.
From Chapter 5·3.B, you know that levered equity is riskier than debt. Also, trust me now when
I claim that if investors are not risk-neutral, the cost of capital is generally higher for riskier
securities. The expected rate of return on risky investments must be higher than the expected
rate of return on safer investments; it must be higher for equity than for debt; and it must be
higher for riskier debt than for safer debt. In the example in this section, we shall assume that
the appropriate expected rate of return for a ¬rm ¬nanced with 50% debt is 7.5% for the debt,
and 12.5% for the remaining 50% “levered equity” (residual ownership).
¬le=comparables.tex: LP
252 Chapter 10. Valuation From Comparables.

The cost of capital for the ¬rm overall remains at 10% after the ¬rm is ¬nanced di¬erently,
Side Note:
because

· + · =
50% 7.5% 50% 12.5% 10%
(10.25)
proportion cost of capital proportion cost of capital cost of capital
· + · = .
of debt for debt of equity for equity for the ¬rm

The cost of capital for the overall company has not changed. Section 21 will discuss this in more detail.




Figure 10.5. Earnings, Interest Payments, and Price-Earnings ratios as a Function of Leverage




10.0
100
Earnings and Interest Payments




9.5
Ear
nin
80




gs




Price/Earnings Ratio

9.0
60




8.5
8.0
40




nts




7.5
me
20




ay
st P
ere
Int




7.0
0




0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Debt/Asset Ratio Debt/Asset Ratio



As the ¬rm™s debt ratio goes up, its interest payments increase, its earnings decrease”and so does its price-earnings
ratio. The same underlying projects can thus have a price-earnings ratio of, say, 7 or 10.



How much total interest payment does the debt have to promise? The loan value is $500, the
The changed
price-earnings ratio interest rate is 7.5%, and payments are forever. Therefore, the perpetuity formula can be solved
under the 50-50 capital
as follows:
structure.
Annual Payment
Annual Payment = $37.50/year
$500 = ’
7.5%
(10.26)
CF
= .
PV
E (r )
Having issued debt, the equity no longer receives $100 per year, but only what is left after
interest payments, i.e., $100 ’ $37.50 = $62.50 per year. Consequently, the price-earnings
ratio of this ¬rm™s equity shares will be the value of the equity (now $500) divided by the
earnings available to equity,

(10.27)
P/E = $500/$62.50 = 8.0 (times) .

In sum, when the same ¬rm is ¬nanced with a 50/50 debt equity ratio, rather than a 0/100
debt equity ratio, its price-earnings ratio is 8 rather than 10. Figure 10.5 shows this graphically
for a whole range of di¬erent debt-asset ratios: the higher the ¬rm™s debt load, the higher the
interest payments, the lower the equity earnings, and the lower the price-earnings ratio. (The
¬gure assumes that the expected [not just the promised!] debt interest rate increases in the
debt-asset ratio according to the formula 5% + 5% · D/A.)



Important: The price-earnings ratio is higher when the ¬rm has lower leverage
(debt-equity ratio).
¬le=comparables.tex: RP
253
Section 10·3. Problems With P/E Ratios.

To compare ¬rms that you deem to be identical in operations, but di¬erent for their capital Revisiting CocaCola,
PepsiCo, and Cadbury:
structures, you need to adjust them to equivalent, unleveraged values. Let us put this insight
Using leverage
to practical use. Assume that the companies of Coca Cola, PepsiCo, and Cadbury Schweppes information to improve
are identical, even if their equities may not be because of their di¬erent leverage ratios. Some valuation.
gathering of information from Yahoo!Finance allows you to put together Table 10.3:


Table 10.3. Financial Information from Yahoo

Leverage Financials, in billion-$
D
Equity
Interest Earn-
D+E
P/E = D/A
STOCK (SYM) D/E Expense EBITDA ings Value
Coca Cola (KO) 35 56% 36% $0.244 $6.14 $3.91 $136.85
PepsiCo (PEP) 34 33% 25% $0.207 $4.26 $2.74 $93.16
Cadbury Schweppes (CSG) 21 49% 33% $0.155 $1.28 $0.72 $15.12

Note: The ¬rm™s asset value A is the sum of its equity value E and debt value D. The formula to translate debt-equity
(D/E) ratios into debt-asset (D/A) ratios is

D+E E D
1 1 1
= = = 1+ ’ = . (10.28)
D/ D/ 1
D D E ’1
(D + E)
A D/A

In general, debt-equity ratios could either be based on the market value of equity or the book value of equity. The
latter is especially problematic”though commonly used.



You are now ready to ask what would happen if the three companies were not leveraged, but Translating P/E ratios of
levered ¬rms into
were ¬nanced only by equity. First, the earnings would not be diminished by the interest
P/E ratios as if unlevered.
expense that the ¬rms are currently paying. You must add back the interest expense to the
earnings to get “as if unlevered” earnings. Second, the market capitalization of equity would
increase. After all, the ¬rm™s projects would no longer be ¬nanced by debt and equity, but by
equity alone. If a ¬rm has a debt/equity ratio of 33% (1/3), for every dollar worth of debt it
currently has 3 dollars worth of equity. Thus, an unlevered equivalent ¬rm would be ¬nanced
with $4 in equity. To convert a debt/value ratio to an unlevered value, divide the (levered) equity
value by one minus the debt/value ratio. In Table 10.4, we can construct “as if unlevered” P/E
ratios by dividing the unlevered ¬rm capitalization by the unlevered equity earnings (all quoted
in billion dollars):


Table 10.4. Computing Unlevered P/E Ratios


STOCK (SYM) (P/E)Lv (P/E)UnLv
Unlevered Earnings Unlevered Value
$3.91 + $0.244 = $4.15 $136.85/(1 ’ 36%) ≈ $214
Coca Cola (KO) 35 52
$2.74 + $0.207 = $2.95 $93.16/(1 ’ 25%) ≈ $124
PepsiCo (PEP) 34 42
$0.72 + $0.155 = $0.88 $15.12/(1 ’ 33%) ≈ $23
Cadbury (CSG) 21 26




These computations are only approximations and wrong for at least two reasons. First, we
Side Note:
assume no taxes. If by unlevering the ¬rm incurred more taxes, these taxes should be subtracted from ¬rm
value. Chapter 22 will discuss the role of corporate taxes in more detail. Fortunately, in this particular case (for
these three companies), not much would change. Second, the unlevering depends on assuming that the ¬rm
continues forever, so that the perpetuity formula is applicable. This could also be wrong. Again, fortunately, in
this particular case (for these three companies), not much would change for other growth assumptions.
¬le=comparables.tex: LP
254 Chapter 10. Valuation From Comparables.

Does it appear as if Cadbury Schweppes (the underlying unlevered company) now is a lot more
Unfortunately, in our
case, after proper like PepsiCo than levered Cadbury Schweppes shares were to levered PepsiCo shares? Unfortu-
adjustment, the
nately, the answer is the opposite of what you should have hoped for. The P/E ratios of Cadbury
P/E ratios have become
Schweppes are even more di¬erent from those of Coca Cola and PepsiCo than they were before.
more different, not
more similar.
You also have some more information to evaluate your earlier remarkable ¬nding that PepsiCo
could be accurately valued with the comparable of Coca Cola. You chose Coca Cola because
you believed that the ¬rm of Coca Cola would be similar to PepsiCo, not that the equity shares
of Coca Cola would be similar to those of PepsiCo. But, in this case, the ¬rms of Coca Cola
and PepsiCo are less similar than the equity shares of Coca Cola and PepsiCo: their unlevered
P/E ratios are farther apart than their levered P/E ratios. So, if you had properly applied the
valuation ratio of one ¬rm to the other ¬rm, you would have concluded that PepsiCo and Coca
Cola are not so similar, after all, and that you should not have compared the two. You just got
lucky. You lived in ignorant bliss.
Solve Now!
Q 10.5 List the main problems with using comparables.


Q 10.6 A ¬rm with a P/E ratio of 20 wants to take over a ¬rm half its size with a P/E ratio of 50.
What will be the P/E ratio of the merged ¬rm?


Q 10.7 The following are quarterly earnings and assets for Coca Cola and PepsiCo:

KO PEP
Earnings (Qua/Ann) Assets (Qua/Ann) Earnings (Qua/Ann) Assets (Qua/Ann)
6/2002 1,290 25,287 888 24,200
3/2002 801 23,689 651 22,611
12/2001 914 3,979 22,417 22,417 667 2,662 21,695 21,695
9/2001 1,074 22,665 627 23,036
6/2001 1,118 22,387 798 19,503
3/2001 873 22,248 570 18,660
12/2000 242 2,177 20,834 20,834 698 2,183 18,339 18,339
9/2000 1,067 23,141 755 17,659
6/2000 926 23,258 668 17,492


If it is now in July 2002, what would be good comparable earnings and comparable assets for
these two ¬rms?


Q 10.8 A ¬rm that is 100% equity ¬nanced is considering a recapitalization to a 50-50 debt-
equity ratio. What will happen to its P/E ratio?


Q 10.9 A ¬rm has a P/E ratio of 12 and a debt-equity ratio of 66%. What would its unlevered
P/E ratio (i.e., the P/E ratio of its underlying business) approximately be?


Q 10.10 On October 9, 2002, the seven auto manufacturers publicly traded in the U.S. were

Manufacturer Market Cap Earnings
Volvo (ADR) $5.7 “$0.18
Ford $14.1 “$5.30
GM $18.8 $1.83
Nissan (ADR) $27.0 $2.55
DaimlerChrysler $32.3 $4.63
¬le=comparables.tex: RP
255
Section 10·4. Other Financial Ratios.

(All quoted dollars are in billions. Ignore leverage. ADR means American Depositary Receipt, a
method by which foreign companies can list on the New York Stock Exchange.) On the same day,
Yahoo! Deutschland reported that Volkswagen AG had earnings of 3.8 billion euro. In terms of
sales, Volkswagen was most similar to Volvo and Ford. What would you expect Volkswagen to be
worth?


Q 10.11 What are the basic assumptions in applying the P/E ratio of one company to the earnings
of another company?



10·4. Other Financial Ratios

Financial ratio analysis is extremely widely used in the real world”unfortunately, often without
a good understanding of what ratios mean, what they do not mean, how they can be put to good
use, and how they can sometimes obscure the right decision. If you do ¬nancial ratio analysis,
be very, very careful. Know what it is that you are doing and think about meaning.
You should now understand that price-earnings ratios are very useful, but they are no panacea.
They have big shortcomings, too. Still, overall, the P/E ratio is the best ratio I am aware of.
However, there are situations in which other value ratios can give you better value estimates.
Moreover, there are non-value based ratios, whose purpose is less to give you an estimate of
value and more to give you intuition about the economics of the ¬rm.


10·4.A. Value-Based Ratios

There are a large number of other ratios in use, and this section presents a potpourri of some Price-earnings ratios are
not the only measure.
popular ones. The list is not exhaustive, as indeed only the imagination limits the quantities
The goal is to ¬nd a
that can be used in the denominator. Two ratios that are relatively similar to the P/E ratio measure that is
discussed in the previous section are proportional to value.


Alternative Price-Earnings or Cash Flow Ratios Earnings can be de¬ned in a variety of ways:
with or without extraordinary items, diluted, etc. There is no right or wrong way: the goal
is to ¬nd a ratio that makes the comparables ¬rm appear to be as similar as possible.
For example, one measure of earnings that from Chapter 9 is EBITDA (earnings before
interest and taxes, depreciation, and amortization). The rationale is that accounting de-
preciation is so ¬ctional that it should not be subtracted out. But EBITDA has problems
with leverage (interest expense) and capital expenditures”if you use it, please subtract
these. Of course, if you do, you will de-facto use a price over cash ¬‚ow ratio, which can
su¬er from the shortcomings that capital expenditures are very “lumpy.” This is why we
used earnings rather than cash ¬‚ows in the ¬rst place.

Price/Book-Value-of-Equity Ratios This ratio is commonly used, and often abbreviated as the
market/book ratio. It should not be recommended for valuation purposes. The reason
is that the book value of equity is often close to meaningless. Accountants use the book
value of equity to balance assets and liabilities, in accordance with all sorts of accounting
conventions (such as depreciation). As a result, this measure is especially di¬erent across
¬rms with di¬erent ages of ¬xed assets (such as buildings).

However, sometimes neither earnings nor the book-value of equity are meaningful. For exam- Many biotech ¬rms have
neither earnings nor
ple, biotech ¬rms may need to be valued even before they have meaningful, positive earnings.
sales. So, what to use?
The idea is to substitute another, more meaningful quantity for earnings. In biotech ¬rms, a
better (but still very bad) measure than earnings may be the number of scientists. An ana-
lyst might ¬nd that biotech ¬rms are worth $1,000,000 per employed scientist. In principle,
the comparables valuation method remains the same as it was when used with price earnings
ratios. The alternative ratio typically still has price (either equity value or overall ¬rm value)
¬le=comparables.tex: LP
256 Chapter 10. Valuation From Comparables.

in the numerator, but a quantity other than earnings (e.g., sales or number of scientists) in
the denominator. The analyst chooses comparable ¬rm(s), determines an appropriate typical
comparables ratio, and ¬nally multiplies this comparables ratio by the ¬rm™s own quantity to
determine its value. This may work well only if ¬rms are comparable enough among the chosen
dimensions that application of the ratio of some ¬rms to the ratio of others o¬ers a meaningful
price.

Price/Sales Ratios This ratio is especially popular for industries that do not have positive earn-
ings. Therefore, it was commonly used during the Internet bubble, when few Internet ¬rms
had positive earnings. Presumably, ¬rms with higher sales should be worth more.
One problem was that ¬rms, such as Amazon during the Internet bubble at the turn of
the millennium, were known to sell merchandise at a loss. Naturally, it is relatively easy
to sell $100 bills for $99! So, the more Amazon sold, the more money it lost”but the
more valuable Amazon appeared to be. After all, with higher sales, the Price/Sales ratio
suggested that Amazon would be worth more.

Price/Employees Ratio This ratio is popular when ¬nancials are deemed not trustworthy. Of
course, it assumes that the employees at the comparable ¬rm are as productive as the
employees in the company to be valued.

Price/Scientists Ratio This ratio is popular for upstart technology ¬rms, which have neither
earnings nor sales. One problem is that it induces ¬rms to hire incompetent scientists on
the cheap in order to increase their valuations. After all, ¬rms with more scientists are
presumed to be worth more.

Price/Anything Else Your imagination is the limit.

This latter set of ratios only makes sense if you compute them for the enterprise value of the
¬rm (that is, the value of all equity plus the value of all debt). If you want to obtain the value
of the equity, you should compute these ratios using the enterprise value, and then subtract
o¬ the current value of all debt.
Solve Now!
Q 10.12 On July 28, 2003 (all quoted dollars are in billions):

Firm Cash Sales Dividends Value D/E
CSG n/a $9.2 $0.4 $12.2 153%
KO $3.6 $20.3 $2.2 $110.8 43%
PEP $1.8 $25.9 $1.1 $81.0 22%

Hansen Natural had $210,000 in cash, $9.22 million in sales, zero dividends, and a debt/equity
ratio of 10%. What would a price/cash ratio predict its value to be? A price/sales ratio? A
price/dividend ratio? Elaborate on some shortcomings.
¬le=comparables.tex: RP
257
Section 10·4. Other Financial Ratios.

10·4.B. Non-Value-Based Ratios Used in Corporate Analyses

Not all ratios are used to estimate ¬rm value. Other ratios can help to assess ¬nancial health Other ratios can be used
to judge health and
and pro¬tability”or can be merely interesting. They can help in the “art” of valuation if they
pro¬tability.
can help you learn more about the economics of the ¬rm. For example, a number of ratios are
often used to judge ¬nancial health (proximity to bankruptcy) and pro¬tability. Most ratios vary
systematically by industry and over the business cycle. Thus, they should only be compared to
similar ¬rms at the same time. On occasion, however, ratios can be so extreme that they can
raise a good warning ¬‚ag. For example, if you ¬nd that the ¬rm has ten times its earnings in
interest to pay, you might become somewhat concerned about the possibility of bankruptcy,
regardless of what is standard in the industry at the time.
Before discussing the ratios, realize that you should be twice as cautious when ratios involve Watch out for the
meaning of book value
quantities from the balance sheet and four times as cautious when they involve the book value
of equity, in particular.
of equity. This quantity is often so far from the true market value that ratios based on the book
value can be almost meaningless. (It is not even a good estimate of replacement value, either.)
The reason is that after accountants have completed all their bookkeeping, this number will
become what is required to equalize the left-hand side and right-hand side of the balance sheet.
It is a “placeholder.”
Without further ado, here are some of the more interesting and common ratios. For each one, We now do ratios on
PepsiCo.
you will ¬nd one or more sample computations for PepsiCo in 2001 (which you can compare to
the ¬nancials from Section 9·1.B), but be aware that many of these ratios exist in various forms.
The ratios are sorted, so that the ones at the top tend to re¬‚ect ¬nancial health and liquidity,
while the ones at the bottom tend to re¬‚ect pro¬tability. www.investopedia.com o¬ers a nice
reference for many of these ratios.
Let us begin with ratios that consider the ¬rm™s debt load. A ¬rm that has high debt ratios Debt-related ratios.
(especially compared to its industry) must often be especially careful to manage its cash and
in¬‚ows well, so as to avoid a credit crunch. Moreover, if you want to borrow more money, then
potential new creditors will be very interested in how likely it is that you will not default. They
will judge your indebtness relative to your pro¬tability, cash ¬‚ow, and industry.

Debt/Equity Ratio The ratio of debt over equity. Many variations exist: debt can be just long-
term debt, all obligations, or any other kind of liability. Equity can be measured either in
terms of book value or in terms of market value.
Long Term Debt 2, 651
= ≈ 3% . (10.29)
PepsiCo, 2001:
Market Value of Equity 87, 407

Long Term Debt 2, 651
= ≈ 31% . (10.30)
PepsiCo, 2001:
Book Value of Equity 8, 648
As stated above, the book value of equity is very problematic. The book value of debt is
usually much better”and, as is not the case with equity, you rarely have access to the
market value of debt, anyway. (If interest rates have not changed dramatically since issue,
this is a good approximation of overall market value.)

All Liabilities 13, 047
= ≈ 15% . (10.31)
PepsiCo, 2001:
Market Value of Equity 87, 407


Debt Ratio As above, but adds the value of debt to the denominator. Because market value of
debt is rarely available, a common variant adds the book value of debt and the market
value of equity. For example,

Long Term Debt 2, 651
= ≈ 2.6% . (10.32)
PepsiCo, 2001:
87, 407 + 13, 047
Market Value of Equity + Debt

Long Term Debt 2, 651
= ≈ 12% . (10.33)
PepsiCo, 2001:
Book Value of Assets 21, 695
¬le=comparables.tex: LP
258 Chapter 10. Valuation From Comparables.


All Liabilities 13, 047
= ≈ 13% . (10.34)
PepsiCo, 2001:
87, 407 + 13, 047
Market Value of Equity + Debt


Interest Coverage The ratio of debt payments due as a fraction of cash ¬‚ows. Many variations
exist: debt payments can be only interest due, or include both principal and interest. Cash
¬‚ows can be any of a number of choices. Popular choices are pure cash ¬‚ows, operating
cash ¬‚ows, net income plus depreciation minus capital expenditures, and net income plus
depreciation. For example,

Short Term Borrowings 354
= ≈ 23% . (10.35)
PepsiCo, 2001:
Cash Flow (Table 9.10) 1, 556


Times Interest Earned (TIE) The earnings before interest (usually also before taxes) divided
by the ¬rm™s interest. In some sense, the inverse of interest coverage.

Times Interest Earned 4, 021
(10.36)
= ≈ 18 .
PepsiCo, 2001:
TIE 219


Current Ratio The ratio of current assets (cash, accounts receivables, inventory, marketable
securities, etc.) over current liabilities (interest soon-due, accounts payable, short-term
loans payable, etc.) is a measure of liquidity. Often interpreted to be “healthy” if greater
than 1.5.

Current Assets (Page 217) 74
(10.37)
= ≈ 0.5 .
PepsiCo, 2001:
Current Liabilities 158

Do not read too much into this ratio. PepsiCo is very healthy, even though its current
ratio is low.

Quick Ratio or Acid-Test is like the current ratio, but deletes inventories from current assets.
It is often considered healthy if it is greater than 1.0. The idea is that you are then likely
to be able to cover immediate expenses with immediate income.

Current Assets (Page 217) 7
(10.38)
= ≈ 0.0 .
PepsiCo, 2001:
Current Liabilities 158

The cash ratio further eliminates receivables from current assets.

Duration and Maturity You have already used these concepts in the bond context, but they
can also apply to projects and even to ¬rms. They can measure what type of investment
the ¬rm is really making”short-term or long-term. This is not an ordinary ratio in that it
requires projections of future cash ¬‚ows.

Turnover The ratio of sales divided by a component of working capital.

• Inventory Turnover”how often your inventories translate into sales.

Net Sales 26, 935
= ≈ 21/year . (10.39)
PepsiCo, 2001:
Inventories 1, 310

Most ¬nancials also provide the components of inventories, so you could further
decompose this.
• Receivables Turnover”how quickly your customers are paying.

Net Sales 26, 935
= ≈ 13/year . (10.40)
PepsiCo, 2001:
Receivables 2, 142
¬le=comparables.tex: RP
259
Section 10·4. Other Financial Ratios.

• Payables Turnover”how quickly you are paying your suppliers.

Net Sales 26, 935
= ≈ 6/year . (10.41)
PepsiCo, 2001:
Payables 4, 461


These measures are sometimes inverted (one divided by the ratio) and multiplied by 365
to obtain a “number of days” measure. For example,

• Days of Receivables Outstanding (DRO), also called Days of Sales Outstanding
(DSO). Accounts Receivables divided by total sales on credit, times number of days
outstanding.

365 · Receivables 365 · 2, 142
= ≈ 29 days . (10.42)
PepsiCo, 2001:
Net Sales 26, 935

PepsiCo collects its bills about every 30 days. A lengthening of this number often
indicates that customers are running into ¬nancial di¬culties, which could impact
PepsiCo negatively.
• Days of Inventories Outstanding. Inventory divided by total sales on credit, times
number of days outstanding:

365 · Inventories 365 · 1, 310
= ≈ 18 days . (10.43)
PepsiCo, 2001:
Net Sales 26, 935

PepsiCo turns over its inventory every 18 days.
• Days of Payables Outstanding (DPO). Accounts Payables divided by total sales on
credit, times number of days outstanding.

365 · Payables 365 · 4, 461
= ≈ 60 days . (10.44)
PepsiCo, 2001:
Net Sales 26, 935

A lengthening of this number could mean that PepsiCo is having di¬culties coming
up with cash to meet its ¬nancial obligations”or found a way to pay bills more
e¬ciently (more slowly in this case).

There are also combined versions, such as the Cash Conversion Cycle, which is the sum
of inventory processing period and the number of days needed to collect receivables. For
PepsiCo, this would be 18 + 29, or about one-and-a-half months.
Turnover ratios and their derivatives (below) are especially important for ¬rms in the
commodities and retail sector, such as Wal-Mart. Good control often allows ¬rms to
leverage economies-of-scale. In this sense, the above measure corporate e¬ciency, and
help managers judge their own e¬ciency relative to their competition.

Pro¬t Margin (PM) or Return on Sales The net or gross pro¬t divided by sales.

Net Income 2, 662
= ≈ 10% . (10.45)
PepsiCo, 2001:
Sales 26, 935

Mature cash cow ¬rms should have high ratios; growth ¬rms typically have low or negative
ratios.

Return on (Book) Assets (ROA), like return on sales, but divides net income by the book value
of assets.
Net Income 2, 662
= ≈ 12% . (10.46)
PepsiCo, 2001:
Book Value of Assets 21, 695
A variant of this measure that adds back interest expense is better, because it recognizes
that assets pay out cash to both shareholders and creditors. Nevertheless, both measures
are dubious, because the book value of assets is often very unreliable. (The book value of
assets contains the book value of equity.)
¬le=comparables.tex: LP
260 Chapter 10. Valuation From Comparables.

Return on (Book) Equity (ROE), like return on sales, but divides net income by the book value
of equity. You also know that I really do not like this measure.

Net Income 2, 662
= ≈ 31% . (10.47)
PepsiCo, 2001:
Book Value of Equity 8, 648


Total Asset Turnover (TAT) A measure of how much in assets is required to produce sales.
Again, with book value of assets in the denominator, this is not a reliable ratio.

Sales 26, 935
= ≈ 1.2 . (10.48)
PepsiCo, 2001:
Assets 21, 695


The DuPont Model multiplies and divides a few more quantities into the de¬nitions of ROA
and ROE:
Net Income Net Income Assets Sales
ROE = = · ·
Book Equity Sales Book Equity Assets
(10.49)
Asset Turnover
Pro¬t Margin Equity Multiplier

Net Income EBIT - Taxes Net Income Assets Sales
= · · · · .
EBIT - Taxes Sales Sales Book Equity Assets

A similar operation can be applied to a variant of ROA:

EBIAT EBIAT Sales
(10.50)
ROA = = · .
Assets Sales Assets
EBIAT is net income before interest after taxes. With book value of assets and book
equity involved, this is often not a particularly trustworthy decomposition, even though
it is mathematically a tautology.
The idea of these decompositions is that they are supposed to help you think about what
the drivers of ROE and ROA are. Again, I do not like this analysis, because I believe that
neither ROA nor ROE are good starting points for an analysis of what drives value. Not
everyone agrees with my opinion here”especially not the individuals administering the
CFA exam, where the DuPont model remains a staple.

Book-to-Market Ratio The book-value of the equity divided by the market value of the equity.
If the book value of equity is representative of how much the assets would cost to replace,
then this is a measure of how much the market values the (special) growth opportunities
that the company has created from replaceable assets.

Book Equity 8, 648
= ≈ 10% . (10.51)
PepsiCo, 2001:
Market Equity 87, 407


Dividend Payout Ratio The paid out dividends divided by earnings. The idea is that a ¬rms
that pays out more earnings today should pay out less in the future, because”in contrast
to a ¬rm that retains earnings”it lacks the paid out cash for reinvestment.

Dividends 994
= ≈ 37% . (10.52)
PepsiCo, 2001:
Net Income 2, 662


Payout Ratio The dividend payout ratio can be broadened to also include share repurchases,
or even net repurchases (i.e., net of equity issuing) to obtain a net payout ratio.

Dividends + Equity Repurchasing 2, 710
= ≈ 100% . (10.53)
PepsiCo, 2001:
Net Income 2, 662

Dividends + Equity Repurchasing - Issuing 2, 186
= ≈ 82% . (10.54)
PepsiCo, 2001:
Net Income 2, 662
¬le=comparables.tex: RP
261
Section 10·4. Other Financial Ratios.

PepsiCo distributed most of its earnings to shareholders.

Dividend Yield The amount of dividends divided by the share price. Dividends can include
share repurchases (in which case, this is called the payout ratio). Dividends are a ¬‚ow
measure, while the stock price is a stock measure. Consequently, dividends can be mea-
sured at the beginning of the period or at the end of the period (in which case, this is called
the dividend-price ratio). Incidentally, stock-¬‚ow timing was also an issue for some of
the measures above, though timing matters more for volatile measures, such as the stock
market value. For example,

Dividends + Equity Repurchasing 2, 710
= ≈ 3.1% . (10.55)
PepsiCo, 2001:
Market Value 87, 407

Firms that have a low payout yield today either have to see smaller stock price increases
in the future (which means a lower expected rate of return), or they have to increase their
payout yield sometime in the future. Otherwise, no one would want to hold them today.

Retention Ratios The retained earnings, divided either by sales, assets, or income. A ¬rm that
decides to start retaining more earnings should pay out more in the future. Because the
retained earnings should be reinvested, such ¬rms should have higher expected earnings
growth. These measures are usually calculated as one minus the dividend payout ratio
or one minus the sum of dividends and equity repurchases divided by net income or
one minus the sum of dividends and net equity repurchases divided by net income. For
example,

2, 662 ’ 2, 710
Net Income - Payout
= ≈ ’0% . (10.56)
PepsiCo, 2001:
Payout 2662

PepsiCo also issued $524 of shares in connection with the Quaker merger, so

2, 662 ’ 2, 710 + 524
Net Income - Net Payout
= ≈ 19% . (10.57)
PepsiCo, 2001:
Net Payout 2, 662

so its retention rate could be judged to be around 19%.

How useful are these ratios? It depends on the situation, the industry, and the particular ratio
for the particular ¬rm”and what you plan to learn from them. If every ¬rm in the industry
has almost the same ratio, e.g., a days of receivables average somewhere between 25 and 32
days, and the ¬rm you are considering investing in reports 7 days, you should wonder about
the economics of this shorter number. Is your ¬rm better in obtaining money quickly? Does
it do so by giving rebates to faster paying customers? Does it mostly work on a cash basis,
while other ¬rms in the industry work on credit? If so, why? Or is your ¬rm simply cooking its
books?
¬le=comparables.tex: LP
262 Chapter 10. Valuation From Comparables.

Closing Thoughts: Comparables or NPV?
10·5.

Should you use comparables or net present value? In practice, comparables enjoy great pop-
Use both valuation
methods, and use ularity, primarily because they do not require much thought. Anyone can look up another
common sense to decide
¬rm™s P/E ratio and multiply it by the earnings of our own ¬rm. In contrast, even a rough NPV
what you believe.
analysis is quite involved. Of course, after reading this chapter, you should understand that
both methods rely on inputs that you will almost surely not know perfectly. You will never
have the perfect comparable, and you will never know the expected future cash ¬‚ow perfectly.
Fortunately, the cause of errors is di¬erent for these two methods. Therefore, if you use both,
you can get a better idea of where the true value lies. This does not mean that you should aver-
age the valuation estimates obtained from NPV and comparables. Instead, you should perform
both analyses, and then take a step back and make up your mind as to which combination of
methods seems to make most sense in your particular situation.
Yes, valuation is as much an art as it is a science. It consists of the tools that you have now
learned and your ability to judge. If you can judge better than others, you will end up a rich
person.




10·6. Summary

The chapter covered the following major points:

• The P/E ratio (price-earnings) is the price of the ¬rm divided by the ¬rm™s earnings, or
equivalently the share price divided by the earnings per share.
Often, these earnings are not the current but the expected earnings.

• The P/E ratio re¬‚ects the ¬rm™s growth opportunities and cost of capital. Higher growth
¬rms have higher P/E ratios.

• P/E ratios and other methods based on comparables can provide an alternative valuation
of ¬rms and projects.

• Comparables su¬er from a variety of problems, some of which can be corrected, and some
of which are intrinsic and uncorrectable.

• Never average P/E ratios. Either average E/P yields and then invert, or divide total multiple-
¬rm values by total multiple-¬rm earnings.

• The comparables valuation techniques and NPV have di¬erent weaknesses, which there-
fore often makes it worthwhile to consider and judge both.

• There are many other ratios that can be used to judge the pro¬tability and the ¬nancial
health of a company. As far as valuation is concerned, their primary purpose is only to
provide useful background information.
¬le=comparables.tex: RP
263
Section A. Advanced Appendix: A Formula For Unlevering P/E ratios.

Appendix




A. Advanced Appendix: A Formula For Unlevering P/E ratios

Return to the example in Section 10·2. Your comparison benchmark ¬rm was Start with a special case
in which ¬rms have
comparable leverage.
P/E
E P
Firm B Financing
100-0 Equity-Debt Financed $100.00 $1,000 10
50-50 Equity-Debt Financed $62.50 $500 8

So, here is your problem: How do you value ¬rm A, if the underlying projects of ¬rm A are
similar to those of ¬rm B? Should you use 8 or 10 as your price-earnings ratio? The answer
is easy if A has the same debt equity ratio as B. Then you can just use the comparison ¬rm™s
price equity ratio as a proxy for your own price equity ratio. That is, if Firm A produced $200
in income for equity holders each year, after ¬nancing with a 50/50 debt equity ratio, then you
would expect its equity value to be about
Price
Implied A Value = · EarningsA
Earnings A

Price
≈ · EarningsA
Earnings B


= 8 · $200 = $1, 600 ,

where we write out Earnings to avoid confusion with equity. As just stated, this equity valuation
depends on the assumption that Firm A had borrowed an equal amount in outstanding debt
($1,600), i.e., that it had a 50/50 debt equity ratio to which you could apply your B multiple.
But what do you do if your A, with its reported income of $200 for equity holders, had borrowed Problem is: leverage may
be different. Try to
$2,500 instead of $1,600? Or, what if A had not borrowed anything? You need to determine an
unlever both.
appropriate comparable that you can apply to A and that takes into account the actual leverage
of A and of B. The easiest method is to convert all price-earnings ratios to a 0/100 debt equity
ratio. In this case, you already know the result that you wish to obtain: a formula should tell
you that unlevering B should translate the previous ratio of 8 into a price-earnings ratio of 10.
Next, you need to look up the interest rate that A is paying for borrowing. Let us assume that
A™s records inform you that the interest rate is 8%. This means that A is paying $200 in interest
each year, before it paid o¬ the $200 to its equity holders. Consequently, you know that a
0/100 debt equity A would have produced earnings of $200 + $200 = $400. Thus,
Price
Implied A Value = · EarningsA
Earnings A

Price
≈ · EarningsA
Earnings B


= 10 · $400 = $4, 000

This would be the value of an all equity ¬rm. Because A has borrowed $2,500, its equity must
be worth $1,500.
¬le=comparables.tex: LP
264 Chapter 10. Valuation From Comparables.

So the trick is to convert all debt equity ratios into “all equity” ratios ¬rst. Unfortunately, there
An attempt at a
delevering formula. is no general formula to do so: the translation formula depends on the time when the cash
¬‚ows are likely to occur. The following formula, based on a plain perpetuity assumption on
the ¬rm™s earnings, often works reasonably well:

A Debt Adjustment Formula for P/E ratios
Debt
1 ’ (rFirm ’ rDebt ) ·
Price Earnings
=
rFirm
Earnings Relevered

Debt PriceFirm
= 1 ’ (rFirm ’ rDebt ) · ·
Earnings EarningsFirm

where “¬rm” means an all-equity no-debt ¬nanced ¬rm. Let us apply this formula to ¬rm B. Let
us assume that you know that B has a value of $1,000 and a price-earnings ratio of 10 when
it has no debt, but it is now considering a move to a 50/50 debt equity ratio. You want to
determine this capital structure change on its new price-earnings ratio. Use the formula:
Price Debt PriceFirm
= 1 ’ (rFirm ’ rDebt ) · ·
Earnings Earnings EarningsFirm
Relevered

$500
= 1 ’ (10% ’ 7.5%) · · 10
$62.50

= [1 ’ 0.025% · 8] · 10


= 0.8 · 10 = 8 .

This formula makes it easy to ¬gure out how an all equity ¬rm™s price earnings ratio changes
when it takes on debt. If you know the debt equity ratio of a ¬rm and want to convert it into a
debt-free equivalent price-earnings ratio, then you can use the following conversion.
To convert the observed leveraged P/E ratio into a hypothetical P/E ratio for an unlevered ¬rm,
the following approximation formula can be helpful:

Price
Earnings Firm
(10.58)
1 Price
= · .
Debt Earnings
1 ’ (rFirm ’ rDebt ) · Equity
Earnings

This formula makes very speci¬c assumptions on the type of ¬rm, speci¬cally that earnings
are a plain perpetuity. The formula can sometimes be a decent approximation if earnings are
not a perpetuity.
¬le=comparables.tex: RP
265
Section A. Advanced Appendix: A Formula For Unlevering P/E ratios.

Solutions and Exercises




1. You would probably value houses by the method of comps”NPV would be exceedingly di¬cult to do. How-
ever, there are often similar houses that have recently sold. You might use a ratio that has price in the numer-
ator and square-foot in the denominator, and multiply this ratio from comparable houses by the square-foot
of your new residence.


2. Microsoft is growing faster, so it would have a higher P/E ratio.
3. E/P = E (˜) ’ E (g) ’ E (˜) = P /E + E (g) = 1/40 + 6% = 8.5%. Therefore, E/P = 8.5% ’ 7% = 1.5% and its
r r
˜ ˜
P/E ratio would shoot from 40 to 66.7. The percent change in value would therefore be 66.6/40 ’ 1 ≈ 66%.
4. E/P = E (˜) ’ E (g) ’ E (g) = E (˜) ’ E/P = 10% ’ 1/20 = 5%.
r r
˜ ˜


5. See the text.
6. Do an example. The acquirer has value of $100, so it needs to have earnings of $5. The target has value of
$50, so it needs to have earnings of $1. This means that the combined ¬rm will have earnings of $6 and value
of $150. Its P/E ratio will thus be 25.
7. Earnings: The TTM Earnings for KO is 3, 979 + (801 ’ 873) + (1, 290 ’ 1, 118) = 4, 079. The TTM Earnings
for PEP is 2, 662 + (651 ’ 570) + (888 ’ 798) = 2, 833. Assets: You would not compute a TTM, but use the
most recent assets: $25,287 for Coca-Cola and $24,200 for Pepsico.
8. You know from the text that the P/E ratio would go down.
9. This question cannot be answered if you do not know the di¬erent costs of capital. For example, if the ¬rm™s
cost of capital is equal to the debt cost of capital, the P/E ratio would not change at all!
Yahoo reported an actual market value of $10.52 billion euros, and an earnings yield of 36.9% (P/E of 2.7).
10.
The easy part is supplementing the table:

Manufacturer Market Cap Earnings P/E ratio E/P yield
Volvo (ADR) $5.7 “$0.18 “31.7 “3.2%
Ford $14.1 “$5.30 “2.7 “37.6%
GM $18.8 $1.83 10.3 9.7%
Nissan (ADR) $27.0 $2.55 10.6 9.4%
DaimlerChrysler $32.3 $4.63 7.0 14.3%
Honda (ADR) $37.7 $3.09 12.2 8.2%
Toyota (ADR) $87.3 $4.51 19.4 5.2%
Sum $222.9 $11.13 25.1 6.0%
Average $31.8 $1.59 3.6 0.9%

The hard part is deciding on a suitable P/E comparable. The ¬rst method (average E/P yield, then invert)
suggests adopting the astronomical ratio of 1/0.9% = 111, due to Ford™s enormous loss in terms of market
capitalization (Ford had $85 billion in sales, and a positive EBITDA of $4.8 billion. But Ford also has ongoing
depreciation on the order of $15 billion per year, but capital and other expenditures on the order of $18 (2001)
to $37 billion (2000 and 1999).) The second method (sum up E™s and P™s ¬rst) suggests $222.9/$11.1 = 20,
but it weighs the larger [and Japanese] ¬rms more highly. Nevertheless, in this case, the second method came
closer to the actual Volkswagen P/E multiple of 27.
Incidentally, by mid-2003, VW had introduced a couple of ¬‚ops, and its earnings had sagged to $2.5 billion,
though its market capitalization had increased to $15 billion. This meant that Volkswagen™s P/E multiple had
shrunk from 27 to 6 in just nine months!
11. The ¬rms are alike substitutes in all respects, including product, product lines, and debt ratio.


12. These ratios are usually performed without debt adjustment”the equivalent of surgery without anesthesia.
This is a huge problem, but it also makes this exercise relatively easy.

Firm Value/Cash Value/Sales Value/Dividends
CSG n/a 1.3 30
KO 185 5.5 50
PEP 45 3.1 74

• The cash-based ratio suggests a value between $10 million and $39 million. The cash-based ratio values
all ¬rms as if only current cash has any meaning, and the ongoing operations are irrelevant (except to
the extent that they have in¬‚uenced current cash).
¬le=comparables.tex: LP
266 Chapter 10. Valuation From Comparables.

• The sales-based ratio suggests a value between $12 million, $29 million, and $50.6 million. Because the
smaller comparables have lower ratios, one might settle on a lower value. The sales-based ratio ignores
that CSG™s equity value is relatively low because more of its value is capitalized with debt than with
equity.
• The dividend-based ratio suggests a zero value. Obviously, this is not a perfect estimate. Firms can
choose di¬erent payout policies.

Hansen™s actual value on this day was $51.4 million.




(All answers should be treated as suspect. They have only been sketched, and not been checked.)
Part III

Investments




There is a long version and short version of the Investments part of the book. You are looking at the long version.
The short version will appear in a dedicated corporate ¬nance version of the book, and can already be downloaded
from the website.
This introduction appears in the Survey text only.




267
269


Transition

We are still plagued by one problem: We do not yet know where the cost of
capital, the E(˜), in the present value formula comes from. We just assumed
r
we knew it.

In the real world, the cost of capital is determined by our investors”and our
investors have many choices. So we have to understand their mindset. They
can put money in bonds, stocks, projects, etc.”or into our ¬rm™s projects. If
investors very much like the alternatives, then our ¬rm™s cost of capital will
be high. Think of our corporate cost of capital as our investors™ Opportunity
Cost of Capital.

To learn more about where the cost of capital comes from, we have to study
not just our own project, but more generally how investors think”what they
like and dislike.

Of course, it is nice that we are often ourselves investors, so learning how to
best invest money in the ¬nancial markets has some nice side bene¬ts.



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